人工智能08不確定性(文件)
【正文】 ? Question: 一個(gè)患者檢測(cè)呈陽(yáng)性 . 該患者得病的幾率是多少 ? ? 025%, 2575%, 7595%, or 95100%? 課堂測(cè)驗(yàn) ? A doctor performs a test that has 99% reliability, ., 99% of people who are sick test positive, and 99% of people who are healthy test negative. The doctor estimates that 1% of the population is sick. ? Question: A patient tests positive. What is the chance that the patient is sick? ? 025%, 2575%, 7595%, or 95100%? ? Intuitive answer: 99%。“你怎么 到這里的？坐火車嗎？” “不，我飛過來的 ” “What about the possibility of a bomb?” “Well, I began thinking that if the odds of one bomb are 1:million, then the odds of two bombs are (1/1,000,000) x (1/1,000,000). This is a very, very small probability, which I can accept. So now I bring my own bomb along!” Conditional independence 條件獨(dú)立性 ? Random variables can be dependent, but conditionally independent ? Example: Your house has an alarm Neighbor John will call when he hears the alarm Neighbor Mary will call when she hears the alarm Assume John and Mary don’t talk to each other ? Is JohnCall independent of MaryCall? No – If John called, it is likely the alarm went off, which increases the probability of Mary calling P(MaryCall | JohnCall) ≠ P(MaryCall) 條件獨(dú)立性 ? But, if we know the status of the alarm, JohnCall will not affect whether or not Mary calls P(MaryCall | Alarm, JohnCall) = P(MaryCall | Alarm) ? We say JohnCall and MaryCall are conditionally independent given Alarm ? In general, “A and B are conditionally independent given C” means: P(A | B, C) = P(A | C) P(B | A, C) = P(B | C) P(A, B | C) = P(A | C) P(B | C) 條件獨(dú)立性 P(Toothache, Cavity, Catch) has 23 1= 7 independent entries 專業(yè)領(lǐng)域知識(shí) : Cavity directly causes toothache and probecatches. If I have a cavity, the probability that the probe catches in it doesn‘t depend on whether I have a toothache: (1) P(catch | toothache, cavity) = P(catch | cavity) The same independence holds if I haven’t got a cavity: (2) P(catch | toothache, 172。a | e) = 1 P(a | e) negation for conditional probabilities 通過枚舉的推理 Start with the joint probability distribution（全聯(lián)合概率分布） : For any proposition φ, sum the atomic events where it is true: 一個(gè)命題的概率等于所有當(dāng)它為真時(shí)的原子事件的概率和 通過枚舉的推理 Start with the joint probability distribution（全聯(lián)合概率分布） : For any proposition φ, sum the atomic events where it is true: 一個(gè)命題的概率等于所有當(dāng)它為真時(shí)的原子事件的概率和 通過枚舉的推理 Start with the joint probability distribution（全聯(lián)合概率分布） : For any proposition φ, sum the atomic events where it is true: 一個(gè)命題的概率等于所有當(dāng)它為真時(shí)的原子事件的概率和 通過枚舉的推理 Start with the joint probability distribution（全聯(lián)合概率分布） : Normalization（歸一化） Denominator（分母） can be viewed as a normalization constant α P(Cavity | toothache) = α P(Cavity, toothache) = α *P(Cavity, toothache, catch) + P(Cavity, toothache, 172。s own state of knowledge ., P(A25 | no reported accidents) = These are not assertions（斷言） about the world 命題的概率隨著新證據(jù)的發(fā)現(xiàn)而改變 : ., P(A25 | no reported accidents, 5 .) = 不確定條件下的決策 假設(shè)下述概率是真的 : P(A25
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